The use of solar faculae in studies of the sunspot cycle

Comparison of the long-term variation of photospheric faculae areas with that of sunspots shows that studies of faculae provide both complementary and supplementary information on the behaviour of the solar cycle. Detailed studies of the development of sunspots with respect to faculae show that there is a high degree of order over much of a given cycle, but marked differences from cycle to cycle. Within a cycle the relationship between spot and faculae areas appears to be similar for the N and S solar hemispheres, and over the early stages of a cycle it is directly related to the magnitude of the maximum sunspot number subsequently attained in that cycle.This result may well have predictive applications, and formulae are given relating the peak sunspot number to simple parameters derived from this early developmental stage. Full application to the current cycle 21 is denied due to the cessation of the Greenwich daily photoheliographic measurements, but use of the cruder weekly data suggests a maximum smoothed sunspot number of 150 ± 22.The effects of the incompatibility of the spot and faculae data, in that faculae are unobservable over a large fraction of the solar disc and also do not always develop associated spots, have been examined in a detailed study of two cycles and shown not to vitiate the results.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

The Relative Phase Asynchronization between Sunspot Numbers and Polar Faculae

The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk and for both hemispheres in solar cycles 19, 20, 21 and 22. We found that (1) the polar faculae begin earlier than sunspot activity, and the phase difference exhibits a consistent behaviour for different hemispheres in each of the solar cycles, implying that this phenomenon should not be regarded as a stochastic fluctuation; (2) the inverse correlation between polar faculae and sunspot numbers is not only a long-term behaviour, but also exists in short time range; (3) the polar faculae show leads of about 50–71 months relative to sunspot numbers, and the phase difference between them varies with solar cycle; (4) the phase difference value in the northern hemisphere differs from that in the southern hemisphere in a solar cycle, which means that phase difference also existed between the two hemispheres. Moreover, the phase difference between the two hemispheres exhibits a periodical behaviour. Our results seem to support the finding of Hiremath (2010).     

Do polar faculae on the sun predict a sunspot cycle?

The paper reports the results of the analysis of the data on polar faculae for three solar cycles (1960–1986) at the Kislovodsk Station of the Pulkovo Observatory and on polar bright points in Ca ii K line for two solar cycles (1940–1957) at the Kodaikanal Station of the Indian Institute of Astrophysics. We have noticed that the monthly numbers of polar faculae and polar bright points in Ca ii K line and monthly sunspot areas in each hemisphere of the following solar cycle have a correlation with each other. A new cycle of polar faculae and polar bright points in the Ca ii K line begins after the polar magnetic field reversal. We find that the smaller the period between the ending of the polar field reversal and the beginning of a new sunspot cycle is, the more intense is the cycle itself. The intensity of the forthcoming solar cycle (cycle 22) and the periods of strong fluctuations in activity expected in this cycle are also discussed.     

The sector structure of the active longitudes in solar cycles

The longitudinal distributions of the polar faculae, bright K Ca⁺ points, and sunspot areas have been investigated in three-year intervals at the minima and maxima of the last five solar cycles in the rotation system which corresponds to the background magnetic field:T = 27.23 days (Mikhailutsa, 1994b). It has been shown that there were three specific features of the polar faculae and bright K Ca⁺ point longitudinal distributions: (1) The longitudes of maxima and minima of the distributions were approximately the same in the last five solar cycles. (2) There were predominantly two opposite longitudinal maxima and two opposite longitudinal minima in the distributions of each hemisphere. (3) The distributions of the northern and southern hemispheres were in opposite phase. The extremes of the sunspot area longitudinal distributions were preferentially between the longitudes of the polar facular extremes. The period of the sector structure rotation was defined more precisely:T = 27.227 ± 0.003 days. The results found can serve as an indication that there is a global foursector structure seated in the solar interior which plays a visible role in the polar facular and sunspot distributions.     

Latitude variations of photospheric activity areas with particular reference to solar faculae

Detailed studies of the development of photospheric activity centres for two solar cycles show that Spörer's Law holds in a very similar form to that applying to sunspots for the faculae which inhabit the sunspot zones. Similar differences between the two solar hemispheres can arise, and it seems to be confirmed that the average latitude of faculae tends to be a few degrees poleward of that of sunspots throughout a given cycle. It is shown that the normal averaging process involved in deriving Spörer's Law obscures a detail which is revealed in a breakdown into the variations within successive narrow latitude strips. These show the existence within a cycle of three separate maxima of activity occurring at different epochs and with different preferred latitudes. The main properties of these maxima are discussed.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley (1991, 2008) as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation co-efficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle ei-ther from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field (as inferred from the faculae data) in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.     

太阳黑子月平均面积数活动周及其特征

我们对第12周至第22周的太阳黑子月平均面积数进行统计分析,并与相应的太阳黑子月平均数相比较,结果表明太阳黑子月平均面积数活动周与太阳黑子月平均数活动周有一定的关系。在多数情况下,太阳黑子出现最大值的时间与太阳黑子面积数出现最大值的时间上不一致;太阳黑子平滑月平均数活动周上升期与太阳黑子平滑月平均面积数上升期在大多数情况下不相同;太阳黑子平滑月平均数活动周平均效果的瓦德迈尔效应(Waldmeiereffect)一般要比太阳黑子平滑平均面积数的活动周明显;文中还对太阳黑子平滑月平均面积数活动周的特征进行了分析。     

A Transfer Function Model for the Sunspot Cycle

The mean annual sunspot record for the time interval 1700–2002 can be considered as a sequence of independent, partly overlapping events, triggered quasi-periodically at intervals of the order of 11 years. The individual cycles are approximated by the step response of a band-pass dynamical system and the resulting model consists of the superposition of the response to the independent pulses. The simulated sunspot data explain 98.4% of the cycle peak height variance and the residual standard deviation is 8.2 mean annual sunspots. An empirical linear relationship is found between the amplitude of the transfer function model for each cycle and the pulse interval of the preceding cycle that can be used as a tool of short-term forecasting of solar activity. A peak height of 112 for the solar cycle 23 occurring in 2000 is predicted, whereas the next cycle would start at about 2007 and will have a maximum around 110 in 2011. Cycle 24 is expected to have an annual mean peak value in the range 95 to 125. The model reproduces the high level of amplitude modulation in the interval 1950–2000 with a decrease afterwards, but the peak values for the cycles 18, 19, 21, and 22 are fairly underestimated. The semi-empirical model also recreates recurring sunspot minima and is linked to the phenomenon of the reversal of the solar magnetic field.     

Intermediate-term periodicities in solar activity

The presence of intermediate-term periodicities in solar activity, at approximately 323 and 540 days, has been claimed by different authors. In this paper, we have performed a search for them in the historical records of two main indices of solar activity, namely, the daily sunspot areas (cycles 12–21) and the daily Zürich sunspot number (cycles 6–21). Two different methods to compute power spectra have been used, one of them being especially appropriate to deal with gapped time series. The results obtained for the periodicity near 323 days indicate that it has only been present in cycle 21, while in previous cycles no significant evidence for it has been found. On the other hand, a significant periodicity at 350 days is found in sunspot areas and Zürich sunspot number during cycles 12–21 considered all together, also having been detected in some individual cycles. However, this last periodicity must be looked into with care due to the lack of confirmation for it coming from other features of solar activity. The periodicity around 540 days is found in cycles 12, 14, and 17 in sunspot areas, while during cycles 18 and 19 it is present, with a very high significance, in sunspot areas and Zürich sunspot number. It also appears at 528 days in sunspot areas during cycles 12–21. On the other hand, it is important to note the coincidence between the asymmetry, favouring the northern hemisphere, of sunspot areas and solar flares during cycle 19, and the fact that the periodicity at 540 days was only present, with high significance, in that hemisphere during that solar cycle.     

Determination of the Rotation Periods of Solar Active Longitudes

There are two types of active longitudes (ALs) in terms of the distribution of sunspot areas: long-lived and intra-cyclic ALs. The rotation period of the long-lived ALs has been determined by a new method in this paper. The method is based on the property of ALs to be maintained over several cycles of solar activity. The daily values of sunspot areas for 1878 – 2005 are analyzed. It is shown that the AL positions remain almost constant over a period of about ten cycles, from cycle 13 to cycle 22. The rotation period was found to be 27.965 days during this period. The dispersion in AL positions is about 26° from cycle to cycle, which is half of the dispersion observed in the Carrington system. The ALs in the growth phase of the activity cycle are more stable and pronounced. The excess in solar activity in the ALs over adjacent longitudinal intervals is about 12 – 14%. It is shown that only one long-lived AL can be observed at one time on the Sun, as a rule.     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

Relationships between photospheric plasma angular velocity and solar activity

An analysis of relationships between latitudinal fine structures of the photospheric plasma differential rotation and solar activity shows that sunspot activity seems to be lower (as measured by the number and extension of sunspot groups) at latitudes where minima of angular velocity appear.     

Variability of the integrated solar K line emission

Conclusion The preliminary results presented in this note seem to demonstrate the facts that the sun observed as a star in the light of the K and H lines is variable, and that this variability is closely related to that of the magnetic field intensity, or to the distribution of magnetic fields, and hence to the distribution of calcium plages or photospheric faculae in the solar atmosphere. This variability will not so much be related to the variation of Wolf's relative sunspot numbers or to the variation of the sunspot area.The applicability of the obtained results for the examination of the late-type stars seems to be evident.     

On the Collective Magnetic Field Strength and Vector Structure of Dark Umbral Cores Measured by the Hinode Spectropolarimeter

We study 7530 sunspot umbrae and pores measured by the Hinode Spectropolarimeter (SP) between November 2006 and November 2012. We primarily seek confirmation of the long term secular decrease in the mean magnetic field strength of sunspot umbrae found by Penn and Livingston (IAU Symp. 273, 126, 2011) between 1998 and 2011. The excellent SP photometric properties and full vector magnetic field determinations from full-Stokes Milne–Eddington inversions are used to address the interrelated properties of the magnetic field strength and brightness temperature for all umbral cores. We find non-linear relationships between magnetic field strength and umbral temperature (and continuum contrast), as well as between umbral radius and magnetic field strength. Using disambiguated vector data, we find that the azimuths measured in the umbral cores reflect an organization weakly influenced by Joy’s law. The large selection of umbrae displays a log-normal size spectrum similar to earlier solar cycles. Influenced by the amplitude of the solar cycle and the non-linear relationship between umbral size and core magnetic field strength, the distribution of core magnetic field strengths, fit most effectively with a skew-normal distribution, shows a weak solar cycle dependence. Yet, the mean magnetic field strength does not show a significant long term trend.     

Structural Invariance of Sunspot Umbrae over the Solar Cycle: 1993 – 2004

Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the National Aeronautics and Space Administration/National Solar Observatory (NASA/NSO) spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for center-to-limb intensity dependence. Log-normal fits to the observed size distribution confirm that the size-spectrum shape does not vary with time. The intensity – magnetic-flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of the cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low-amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as manifested by the invariant size-magnetic field relationship, as well as the mean size (i.e., strength) of sunspot umbrae do not significantly depend on the solar-cycle phase.     

Plasma motion in umbrae and the surrounding photosphere derived from spectroscopic Doppler measurements and tracer measurements of spots

The rotational velocity of the Sun is determined by sunspot tracings and by spectroscopic measurements of the photospheric plasma using the non-Zeeman-split line Fe i 5576 and absolute iodine reference. Stationary line shifts as limb-effect and longperiodical shifts introduced by supergranulation are discussed. The dependence on solar activity as Ca⁺ emissivity and magnetic fields is investigated including line asymmetries. The results are: (a) The non active photospheric regions rotate with 1995 ± 30 m s^-1. Solar active regions yield a 60 m s^-1 higher value. (b) In quiet regions the absolute limb shift varies between 170 m s^-1 at the line core and 310 m s^-1 at I/I _cont 0.8 (C-shape); thus the limb shift is mainly due to entire line shifts. (c) In solar active regions (close to spots) asymmetries are widely reduced in line cores; this effect cannot be associated with a variation of the limb effect due to a large scatter of Doppler shifts near spots. (d) A reduced limb shift of 50 m s^-1 is found in network boundaries and is mainly due to a small scale downflow. (e) Observations with a smaller influence of stray light yield symmetric profiles in umbrae. (f) Differences between umbral rotation rates from tracer and spectroscopic measurements do not exceed 20 m s^-1, when considering straylight. The rotational velocity from umbrae exceeds that from the photosphere by 30–60 m s^-1. Some individual spots yield nearly the same rotation rate as the photosphere.     

Sunspots with the Strongest Magnetic Fields

The strongest observed solar magnetic fields are found in sunspot umbrae and associated light bridges. We investigate systematic measurements of approximately 32 000 sunspot groups observed from 1917 through 2004 using data from Mt. Wilson, Potsdam, Rome and Crimea observatories. Isolated observations from other observatories are also included. Corrections to Mt. Wilson measurements are required and applied. We found 55 groups (0.2%) with at least one sunspot with one magnetic field measurement of at least 4000 G including five measurements of at least 5000 G and one spot with a record field of 6100 G. Although typical strong-field spots are large and show complex structure in white light, others are simple in form. Sometimes the strongest fields are in light bridges that separate opposite polarity umbras. The distribution of strongest measured fields above 3 kG appears to be continuous, following a steep power law with exponent about −9.5. The observed upper limit of 5 – 6 kG is consistent with the idea that an umbral field has a more or less coherent structure down to some depth and then fragments. We find that odd-numbered sunspot cycles usually contain about 30% more total sunspot groups but 60% fewer >3 kG spots than preceding even-numbered cycles.     

Reconstruction of the Heliospheric Current Sheet Tilts Using Sunspot Numbers

We have investigated the correlation between the relative sunspot number and tilt of the heliospheric current sheet (HCS) in solar cycles 21–23. Strong and highly significant positive correlation (r > 0.8, P < 0.001) was found for corresponding data in the time interval from May 1976 through December 2004. Cross-correlation analysis does not reveal any time shift between the data sets. Reconstructed values of the HCS tilt, for the time interval before 1976, are found using sunspot numbers. To take different amplitude of solar cycles into account they were then normalized to zero in the minima of the solar activity and to average in solar cycles 21–23 maximal calculated HCS tilt in the maxima. These normalized reconstructed HCS data are compared with the angular positions of the brightest coronal streamers observed during total solar eclipses in 1870–2002, and their agreement is better for the minima of the solar activity than for the maxima.     

Latitudinal Distribution of Polar Faculae

The distribution of polar faculae with respect to latitude is investigated, using data obtained at the Ussuriysk Observatory during the years 1963–1994. To correct the data for the effect of visibility, a visibility function of polar faculae is derived. Corrected surface density of polar faculae is calculated as a function of latitude and time. During most part of each solar cycle, polar faculae exhibit pronounced concentrations at high latitudes with maxima of the surface density located near the poles. Such concentrations of polar faculae (below referred to as `polar condensations') are formed after a lapse of 1–2 years from the polar magnetic field reversals, and then they persist for 7–9 years, until the high-latitude magnetic fields again start to reverse. During several years after the sunspot minima, the polar condensations co-exist with the new latitudinal belts of polar faculae which appear at middle latitudes and then migrate toward the poles. To describe the evolution of the polar condensations quantitatively, the polar faculae density n at latitudes above 60° has been approximated by means of the power law nn ₀ cos^m where is polar angle. The parameters n ₀ and m both are found to vary during the course of the solar cycle, reaching maximum values near or shortly after the minimum of sunspot activity. At the minimum phase of the solar cycle, on average, the surface density of polar faculae varies as cos¹⁴. In addition to the 11-yr variation, the latitude–time distribution of polar faculae exhibits short-term variations occurring on the time scale of 2–3 years.     

Coronal Activity During the 22-Year Solar Magnetic Cycle

The existence of a 22-year heliomagnetic cycle was inferred long ago not only from direct measurements of the solar magnetic field but also from a cyclic variability of a number of the solar activity phenomena. In particular, it was stated (a rule derived after Gnevyshev and Ohl (1948) findings and referenced as the G–O rule in the following) that if sunspot number Rz cycles are organized in pairs of even–odd numbered cycles, then the height of the peak in the curve of the yearly-averaged sunspot numbers Rz-y is always lower for a given even cycle in comparison with the corresponding height of the following odd cycle. Exceptions to this rule are only cycles 4 and 8 which, at the same time, are the nearest even cycles to the limits of the so-called Dalton minimum of solar activity (i.e., the 1795–1823 time interval). In the present paper, we are looking for traces of the mentioned G–O rule in green corona brightness (measured in terms of the Fexiv 530.3 nm emission line intensity), using data covering almost five solar cycles (1943–1994). It was found that the G–O rule seems to work within the green-line corona brightness, namely, when coronal intensity measured in an extended solar middle-latitude zone is considered separately from the rest of the solar surface. On the other hand, the same G–O rule is valid at the photospheric level, as the heliographic latitudinal dependence of sunspot numbers (1947–1984) shows.